$\begin{aligned} &P = -4b^2+6b-9 \\\\ &Q = 7b^2-2b-5 \end{aligned}$ $P-Q=$
Since we are asked to find $P-Q$, let's substitute in the trinomial expressions that we are given for $P$ and $Q$ : $P-Q = (-4b^2+6b-9)-(7b^2-2b-5)$ Since we are subtracting, it is helpful to distribute the $\text{{negative sign}}$ across all terms in the second trinomial: $\begin{aligned}&(-4b^2+6b-9){-}(7b^2-2b-5)\\ \\ =&(-4b^2+6b-9){-}7b^2{-}(-2b){-}(-5)\\ \\ =&-4b^2+6b-9-7b^2+2b+5 \end{aligned}$ Note that the parentheses around the first trinomial don't affect the order of operations, so we can just remove them. When we add or subtract terms in a polynomial expression, the only way that we can simplify the expression is by combining those terms that are alike. Our expression contains terms of $3$ different degrees in the same variable: ${x^2}, {x},$ and the $\text{{constant}}$ term: ${{-4b^2} {+6b} {-9} {-7b^2} {+2b} {+5}}$ Now that we have identified like terms, let's combine them. Make sure to keep track of positive and negative signs! ${{(-4-7)b^2} + {(6+2)b} + {(-9+5)}}$ When we add the coefficients in front of each term, we get the following trinomial: ${-11b^2 +8b -4}$